Fuel Source Thermal Model

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Description

The Fuel Source Thermal Model is a specialized Thermal Model designed for fuel tanks that uses ideal gas law thermodynamics to model temperature and pressure changes during fuel transfer operations. When propellant flows in or out of a tank, the ullage gas (the pressurized gas space above the liquid propellant) undergoes expansion or compression, causing temperature changes captured by this model using adiabatic process equations.

This model attaches to a Fuel Source and tracks the ullage volume, computing pressure and temperature based on the ideal gas law and adiabatic relations. It is typically used for pressure-fed propulsion systems where accurate tank pressure modeling is required.

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Example Use Cases

• Tank Pressure Prediction: Monitor propellant tank pressure throughout a mission to verify adequate feed pressure to thrusters.
• Thermal Budget Analysis: Account for ullage gas temperature changes during propellant consumption or transfer.
• On-Orbit Refueling: Model tank heating during propellant loading operations.
• Propulsion System Design: Validate pressurization system sizing by modeling pressure decay during burns.

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Module Implementation

The model tracks the ullage gas state using thermodynamic relationships for an ideal gas undergoing adiabatic processes.

Tank Geometry

The tank is modeled as a cylinder with volume:

$$V_{\text{tank}}=\pi R^{2}L$$

where $R$ is the tank radius and $L$ is the tank length (from the parent Fuel Source).

Ullage Volume

The ullage volume is the gas space remaining after accounting for liquid propellant:

$$V_{\text{ullage}}=V_{\text{tank}}-\frac{m_{\text{fuel}}}{{\rho }_{\text{fuel}}}$$

where $m_{\text{fuel}}$ is the current propellant mass and ${\rho }_{\text{fuel}}$ is the liquid propellant density. A minimum ullage volume (MinimumUllageVolume) is enforced to prevent numerical instabilities when the tank is nearly full.

Ideal Gas Law

The pressurant gas mass is calculated at initialization using the ideal gas law:

$$m_{\text{gas}}=\frac{P_0{V}_0}{R_{\text{gas}}{T}_0}$$

where $P_0$ is the initial tank pressure, $V_0$ is the initial ullage volume, $R_{\text{gas}}$ is the specific gas constant for the pressurant, and $T_0$ is the initial temperature.

During simulation, the tank pressure is computed from the current state:

$$P=\frac{m_{\text{gas}}{R}_{\text{gas}}T}{V_{\text{ullage}}}$$

Adiabatic Temperature Change

When the ullage volume changes due to propellant flow, the gas undergoes adiabatic expansion or compression. The temperature change follows:

$$\frac{T_2}{T_1}={\left(\frac{V_1}{V_2}\right)}^{\gamma -1}$$

where $\gamma$ is the heat capacity ratio (ratio of specific heats) for the pressurant gas. For propellant expulsion (increasing ullage volume), the gas expands and cools. For propellant loading (decreasing ullage volume), the gas compresses and heats.

Inlet Enthalpy Heating

During propellant fill operations, the incoming propellant may be at a different temperature than the ullage gas. When InletTemperature is set and propellant is flowing in, an additional heating term is applied:

$${\dot{Q}}_{\text{inlet}}={\dot{m}}_{\text{in}}\cdot c_p\cdot (T_{\text{inlet}}-T_{\text{gas}})$$

This captures the dominant heating effect observed during transient propellant loading.

Equivalent Thermal Power

The total temperature change is converted to an equivalent power for integration by the Thermal System:

$$P_{\text{gen}}=m_{\text{gas}}{c}_p\frac{dT}{dt}+{\dot{Q}}_{\text{inlet}}$$

where $c_p$ is the specific heat capacity of the pressurant gas at constant pressure. The first term is positive for compression heating and negative for expansion cooling.

Thermal Mass

The thermal mass of the ullage gas is:

$$C_{\text{th}}=m_{\text{gas}}{c}_p$$

This value is used by the thermal system to compute temperature changes from net heat flow.

Propellant Presets

Convenience methods are provided to configure the model for common propellants and pressurant gases:

Method	Gas/Propellant	Default Initial Pressure
ConfigureAsXenon	Xenon (electric propulsion)	2.0 MPa
ConfigureAsHydrazine	Hydrazine monopropellant	1.5 MPa
ConfigureAsMmhN2o4	MMH/N2O4 bipropellant	1.5 MPa
ConfigureAsHelium	Helium pressurant	3.0 MPa
ConfigureAsNitrogen	Nitrogen pressurant	2.0 MPa

These methods set the gas constant, gamma ratio, specific heat, and optionally the liquid fuel density to appropriate values.

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Assumptions/Limitations

• The model assumes an ideal gas pressurant with constant specific heat properties.
• Adiabatic process assumptions apply; heat transfer between ullage gas and tank walls is handled separately through thermal connections.
• The tank is modeled as a simple cylinder; complex tank geometries are not supported.
• Propellant vapor pressure and two-phase effects are not modeled.
• The pressurant gas mass remains constant; blow-down and regulated pressurization modes behave identically.
• Temperature is clamped between 1 K and 5000 K to prevent numerical issues.

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References

1. Sutton, George P., and Oscar Biblarz. Rocket Propulsion Elements. 9th ed. Wiley, 2017.

2. Huzel, Dieter K., and David H. Huang. Modern Engineering for Design of Liquid-Propellant Rocket Engines. AIAA, 1992.